Abstract
We consider a problem for a first-order differential equation in a Hilbert space. We replace the initial data with some condition that includes the integral of the solution over the entire time interval on which we solve the problem. It is proved that the problem has a unique solution on an arbitrary time interval under the condition that some of the data are positive.
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 2, pp. 417–421. https://doi.org/10.33048/smzh.2021.62.212
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Starovoitov, V.N. Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data. Sib Math J 62, 337–340 (2021). https://doi.org/10.1134/S0037446621020129
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DOI: https://doi.org/10.1134/S0037446621020129